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Modified ADM1 for dry and semi-dry anaerobicdigestion of solid organic wasteFlavia Liottaa, Patrice Chatellierb, Giovanni Espositoa, Massimiliano Fabbricinoc, LuigiFrunzod, Eric D. van Hullebusche, Piet N. L. Lensf & Francesco Pirozzica Department of Civil and Mechanical Engineering, University of Cassino and the SouthernLazio, via Di Biasio 43, 03043 Cassino (FR), Italy.b Université Paris-Est, IFSTTAR, 14-20 Boulevard Newton Cité Descartes, Champs sur MarneF-77447 Marne la Vallée, Cedex 2, France.c Department of Civil, Architectural and Environmental Engineering, University of NaplesFederico II, via Claudio 21, 80125 Naples, Italy.d Department of Mathematics and Applications Renato Caccioppoli, University of NaplesFederico II, via Cintia, Monte S. Angelo, 80126 Naples, Italye Université Paris-Est, Laboratoire Géomatériaux et Environnement, EA 4508, UPEM, 5 bdDescartes, 77454 Marne-la-Vallée, Cedex 2, France.f Core Pollution Prevention and Control, UNESCO-IHE, UNESCO-IHE, Institute for WaterEducation, PO Box 3015, 2601, DA Delft, The Netherlands.Accepted author version posted online: 14 Oct 2014.

To cite this article: Flavia Liotta, Patrice Chatellier, Giovanni Esposito, Massimiliano Fabbricino, Luigi Frunzo, Eric D. vanHullebusch, Piet N. L. Lens & Francesco Pirozzi (2014): Modified ADM1 for dry and semi-dry anaerobic digestion of solidorganic waste, Environmental Technology, DOI: 10.1080/09593330.2014.965226

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Publisher: Taylor & Francis Journal: Environmental Technology DOI: 10.1080/09593330.2014.965226

Modified ADM1 for dry and semi-dry anaerobic digestion of solid organic

waste

Flavia Liotta*, Patrice Chatellier**, Giovanni Esposito*, Massimiliano Fabbricino***, Luigi

Frunzo**** , Eric D. van Hullebusch*****, Piet N. L. Lens******, Francesco Pirozzi***

*Department of Civil and Mechanical Engineering, University of Cassino and the Southern Lazio,

via Di Biasio 43, 03043 Cassino (FR), Italy.

**Université Paris-Est, IFSTTAR, 14-20 Boulevard Newton Cité Descartes, Champs sur Marne F-

77447 Marne la Vallée, Cedex 2, France.

*** Department of Civil, Architectural and Environmental Engineering, University of Naples

Federico II, via Claudio 21, 80125 Naples, Italy.

**** Department of Mathematics and Applications Renato Caccioppoli, University of Naples

Federico II, via Cintia, Monte S. Angelo, 80126 Naples, Italy

***** Université Paris-Est, Laboratoire Géomatériaux et Environnement, EA 4508, UPEM, 5 bd

Descartes, 77454 Marne-la-Vallée, Cedex 2, France.

******Core Pollution Prevention and Control, UNESCO-IHE, UNESCO-IHE, Institute for Water

Education, PO Box 3015, 2601, DA Delft, The Netherlands.

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(*) Corresponding author

E-mail address: flavia.liotta@unicas.it

Tel: 0039. 0776. 299.4339

Fax: 0039. 0776. 299.3939

Abstract

The role of Total Solids (TS) content in anaerobic digestion of selected complex organic matter,

e.g. rice straw and food waste, was investigated. A range of TS from wet (4.5%) to dry (23%) was

evaluated. A modified version of the Anaerobic Digestion Model No.1 for complex organic

substrate is proposed to take into account the effect of the TS content on anaerobic digestion. A

linear function that correlates the kinetic constants of three specific processes (i.e. disintegration,

acetate and propionate up-take) was included in the model. Results of biomethanation and volatile

fatty acids production tests were used to calibrate the proposed model. Model simulations showed

a good agreement between numerical and observed data.

Keywords: dry anaerobic digestion; food waste; mathematical modelling; rice straw; total solids;

ADM1

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1. Introduction

Experimental research carried out in recent years on AD has definitely established that the Total

Solids (TS) content plays an important role on process development [1-4]. As a consequence,

several studies have been carried out recently to adapt and calibrate the existing AD mathematical

models to take into account the effect of the TS content [4-7]. Le Hyaric et al. [4] and Lay et al.

[6] applied the Gompertz model to simulate the results of specific methanogenic activity tests and

found that a high TS content (15%-25%) reduces substrate degradation because of water and

nutrients limitation, resulting in a lower methanogenic activity. Brown et al. [7] used the first-

order kinetic models to characterize the methane production of lignocellulosic biomass and found

a linear relationship between logarithmic methane production and reaction time in both wet and

dry anaerobic digestion of switchgrass, corn stover, wheat straw, leaves, yard waste and maple.

Dry anaerobic digestion generally exhibits a poor startup performance, thus several models

assume the hydrolysis as a rate-limiting step of the process [2]. In particular, Abbassi-Guendouz et

al. [8] applying the Anaerobic Digestion Model N°1 (ADM1) [9] to cardboard treatment, found a

decreasing first-order hydrolysis rate constant for carbohydrates degradation when increasing the

TS content between 15-30%. Liotta et al. [3] also found a decreasing disintegration rate constant

when increasing the TS content in the range of wet digestion.

However all these models do not take into account the role of Volatile Fatty Acid (VFA) uptake

on the mathematical model of dry and semi-dry AD. Recent studies demonstrated the important

role of the mechanisms associated with VFA uptake on process performances [2, 3]. Moreover, for

easily biodegradable wastes such as Food Waste, hydrolysis can not necessarily be the rate-

limiting step of the process [10] As intermediate products, VFA have been treated as an indicator

of the digestion efficiency, but high concentrations of VFA can determine a decrease of pH

leading to performance failure of the digester [2, 7, 11]. An attempt was done by Guendouz [12],

who found a transitory accumulation of VFA during the batch tests, indicating that hydrolysis is

not the sole rate-limiting step of dry AD of organic solid wastes. Motte et al. [13] proposed a

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quadratic model able to dynamically describe the effect of TS, particle size and substrate/inoculum

ratio on methane production, pH and VFA concentration. The model results were accurate (p-

value < 0.05) with a coefficient of determination of 80%. However this model does not take into

account the effect of TS on kinetic constants and it is not an ADM1-like model as it does not

consider all biochemical processes of AD.

The aim of the present article is to develop a kinetic model that can specifically characterize the

disintegration, the acetogenesis and methanogenis steps of selected complex organic substrates as

a function of TS content in order to predict and interpret results from anaerobic digesters in wet,

semi-dry and dry AD. In the following section, an overview of the model structure, assumptions

and main model parameters is presented. The proposed model is based on the cited ADM1 model

[9] as modified by Esposito et al. [14-16] for complex organic substrates. The kinetic equations

are reformulated to consider the direct effect of TS content and the effect of the intermediate

compounds, which can affect, as a function of the TS content, the whole process development.

The dynamics of acetate, propionate and methane production obtained from two different series of

batch tests on AD of food waste and rice straw were used to calibrate the proposed model. Food

waste was selected as a representative of easily, highly biodegradable and heterogeneous

substrates, while rice straw as representative of slowly biodegradable and models of

lignocellulosic residues.

2. Materials and Methods

2.1 Model description

The proposed model is based on a modified version of the ADM1 proposed by Esposito et al.

[14- 16] to take into account the presence of complex organic substrates in the feedstock and the

operation of the digester in semi-dry and dry conditions. It is applied to Completely Stirred Tank

Reactor (CSTR) with a constant feed and to batch systems.

The model proposed by Esposito et al. [14-16] is a structured biological model that simulates the

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major conversion mechanisms of organic substrates into biogas and the degradation of by-

products. It assumes that composite materials are converted into carbohydrates, proteins and

lipids by a disintegration step [14, 17,18]. These components are further hydrolysed into simple

sugars, amino acids and long chain fatty acids. Then, during the acidogenic step, fermentative

micro-organisms convert these products into acetic, propionic, butyric and valeric acids,

hydrogen and carbon dioxide. The uptake of fatty acids yields acetate (acetogenic step), which is

converted into methane by methanogens.

The disintegration and hydrolysis steps are modelled by first-order kinetics. In particular, surface

based kinetics are used for disintegration and a classical first order kinetics for hydrolysis. All

the other transformations are classical biochemical transformations performed by specific

bacterial groups, and are described by a Monod-type equation, where the substrate uptake is

associated with the microbial growth. The kinetics of microbial growth and decay are also

included in the model.

The overall model consists of 28 mass balance equations [9] applied to the 28 state variables (13

substrates and 15 biomasses) summarized in Table 1. The kinetic constants and processes of the

modelled substrates are listed in Table 2. It is worth noting that, according to the model

proposed by Esposito et al. [14-16] only the parameter Ksbk, not included in the original version

of the ADM1, is a function of the substrate intrinsic characteristics, and therefore depends also

on the TS content of the substrate [3].

With respect to the model proposed by Esposito et al. [14-16], this model modifies some of the

kinetic equations listed in Tables A.1-A.2. The kinetic constants (Ksbk, Kac and Kpro) are

expressed as function of the TS content in order to take into account the TS effect on the rates of

substrate disintegration and acetate and propionate up-take. Assuming CSTR conditions and a

constant reactor Volume (V), for each state variable (Ci), the mass balance has the following

form

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dCi

dt= qCi−in

V− qCi−out

V+ ν ijρ j

j=i

23

(1)

where:

the term qCi−in

V− qCi−out

V = 0 in batch conditions, where the flow rate (q) is assumed to be zero,

and the term ν ijρ j

j=i

23

is the overall reaction term expressed as a sum of specific kinetic rate for

the process j ( j) multiplied by the stoichiometric coefficients ( ij) that describes the influence of

the specific process j on the individual component i.

The specific kinetic rates and the stoichiometric coefficients used in the present model are strictly

equivalent to those used in the model proposed by Esposito et al. [14-16] and are listed in Tables

A.1-A.2.

The main originality of the proposed model is the capability to consider the variation of the

kinetic constants Ksbk, Kac and Kpro with the TS content. These constants are involved in the

following specific kinetic rates:

ρ i,1 = Ksbk ⋅C ⋅ a * (2)

ρ i,13 = Kpro ⋅Spro

Ks + Sbu

⋅ Xpro ⋅ I2 (3)

ρ i,14 = Kac ⋅ Sac

Ks + Sac

⋅ Xac ⋅ I3 (4)

These equations have been reformulated by substituting the kinetic constants Ksbk, Kac and Kpro

with the following functions:

Ksbk (TS) = a ⋅TS + b (5)

Kac,pro(TS) = c ⋅TS + d (6)

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where the new parameters a, b, c and d need to be calibrated depending on the substrate type (in

this study rice straw and food waste) and the specific experimental conditions such as

temperature, pressure, pH, retention time and mixing conditions [4].

2.2. Model calibration

The proposed model was calibrated using the experimental data obtained during anaerobic

digestion of food waste and rice straw. The experimental tests were conducted in batch, at 32°C,

using two liter reactors. The following total solids concentrations were tested: 4.2%, 12.8% and

19.2% for the food waste, and 4.8%, 14.8% and 23.4% for the rice straw. The experimental

procedure and the obtained results are reported elsewhere [11,19].

The calibration was performed in two steps. In the first step, the simulated curves were plotted

for each value of Kac, Kpro and Ksbk, and the simulated results were compared with experimental

data by applying the Root Mean Square Error (RMSE) method, as usually done for the model

calibration [16, 20]. In the second step, the values of Kac, Kpro, Ksbk , associated with the lower

RMSE, that better fit the proposed equations (5, 6), were introduced in the model to perform a

second set of simulations. These modelling results were again compared with experimental data

by individuating the final RMSE values for each Kac, Kpro and Ksbk value. The final results of

calibration procedure are summarized in Figures 1-2 and Table 3. In particular the experimental

data were used for both substrates to calibrate the disintegration kinetic constant Kdis of the

ADM1, assuming it coincides with the constant Ksbk of the model proposed by Esposito et al.

[14-16] as the specific surface did not vary in the different tests. Acetic and propionic acid

productions were used to calibrate the constants Kac and Kpro. All the other constants and

parameters were set from literature data [9, 14-16].

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3. Results and discussion

Table 3 and Figure 3a show that for both substrates the calibrated disintegration rate constant

linearly decreased with increasing TS concentration for both substrates. The linear function (5)

can be expressed in this case as follows:

for food waste: Kdis = −0.31⋅TS + 7.92 with r2 = 0.99 (7)

for rice straw: Kdis = −0.1⋅TS + 2.9 with r2 = 0.97 (8)

Where Kdis is assumed to be coincident with Ksbk.

The values of parameters a and b (5) that describe the specific experimental conditions are

different for the two tested substrates because of the specific characteristic of the initial substrate

to be hydrolysed. Food waste is a more easily biodegradable substrate compared to rice straw

that has a complex lignocellulosic structure that is more difficult to be disintegrated. The

structure of rice straw consists of different types of polymers that are difficult to degrade such

as: cellulose (37.4%), hemi-cellulose (44.9%), lignin (4.9%) and silicon ash (13,0%) [21]. In

particular the high lignin content makes the rice straw degradation very difficult as the ligno-

carbohydrate complexes form strong bonds and the plant cell wall is resistant to microbial attack

[22]. Thus for each TS the rice straw disintegration rate constant and the values a, b are lower

than the values of food waste. These results are consistent with results previously presented by

Liotta et al. [3], where a linear correlation with r2 = 0.99 was found between the carrot waste

disintegration rate constant and TS in the range of wet conditions.

The linear correlations (7, 8) describe the slowing-down of the disintegration process at higher

values of the TS content caused by the lack of water and the limited transfer of hydrolysis

products (and other intermediates) to bacterial sites [6, 23, 24]. This is in agreement with results

presented by Liotta et al. [3], Abbassi-Guendouz et al. [8], Pommier et al. [24], who observed a

strong impact of the total solids content on biodegradation kinetic rates and maximum methane

production in anaerobic digestion of different substrates.

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Figure 3b shows that for both substrates, a linear and inverse correlation exists between the

values of the propionate and acetate up-take kinetic constants and the TS content. In this case, a

unique linear function, as reported in (6), can be expressed for acetate and propionate as follows:

for food waste: Kac/ pro = −0.41⋅TS +10.35 with r2 > 0.99 (9)

for rice straw: Kac/ pro = −0.28 ⋅TS +10.71 with r2 > 0.97 (10)

The values of parameters c and d (6) that describe the specific experimental conditions are the

same for acetate and propionate. This means that the kinetic rate constants for acetate and

propionate are equivalent for each TS content. Thus, it can be concluded that the effect of the

water content on propionate and acetate up-take is equal.

Also in this case the parameters c, d differ for different initial substrate types because of

different experimental conditions and biomass involved in the anaerobic degradation of food

waste and rice straw. Additionally there are larger differences between the values of Kac/pro for

rice straw and food waste when the TS is higher. Thus, the intrinsic characteristics of the

substrate type are more effective on the process development and biomass selection in the case

of lack of water.

This study shows that with a higher TS content lower values of Kac/pro are obtained that determine

higher concentrations of acetate and propionate during the whole process (Figures 1-2). This

means that a higher TS content can lead to process inhibition due to VFA accumulation, implying

lower process efficiency in terms of VS degradation, final methane yield and specific methane

production rate. Indeed, Figures 1 and 2 show a lower level of inhibition for the experiments under

wet digestion conditions (TS = 4.52% for food waste, and TS = 4.85% for rice straw), compared

to the experiments under semi-dry (TS = 12.87% and TS = 14.86%) or dry (TS = 19.2% and TS =

23.4%) anaerobic conditions. This is probably due to a reduction of the water content that implies

less contact with biomass because of the more heterogeneous conditions and less availability,

uptake and diffusion of nutrients through the porous medium to bacterial sites [3, 4, 6]. Moreover

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the lower water content can increase the acetate concentration and inhibit methanogens, resulting

in accumulation of propionate and other VFA.

Despite the good fitting between simulated and experimental concentrations, showing the

capability of the model to simulate the AD process of the two substrates with different initial TS,

it is worth noting that the model fitting is of higher quality for the data obtained during rice

straw digestion. For food waste, Figures 1 c, g, k show that some points could not be fitted by

the simulated curves. This means that an inhibition phenomenon, related to the difficult

degradation of propionic acid and consequent formation of propionate isomers during the

process, not taken into account in the simulation, should be considered in the further

development of the kinetic equations of the model. This different behaviour can be related to the

nature of the substrate type. Food waste has a complex nature and contains many different

compounds that have different degradation kinetics [25-28]. In contrast, the kinetic degradation

of the mono-substrate rice straw is more easy to model.

4. Conclusions

A mathematical model capable to simulate semi-dry and dry AD of selected complex organic

substrates such as rice straw and food waste is proposed. Model calibration resulted in the

determination of the kinetic constants of disintegration, acetate and propionate up-take for

different TS contents in the range 4.5%-23%. The good fitting of the biomethanation data with

the model simulation results for both methane production and VFA concentrations confirms the

suitability of the model. Three linear equations that correlate the TS content with the

disintegration and the up-take kinetic constants for acetate and propionate were included in the

model.

Acknowledgements

The authors would like to thank the European Commission for providing financial support through

the Erasmus Mundus Joint Doctorate Programme ETeCoS3 (Environmental Technologies for

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Contaminated Solids, Soils and Sediments) under the grant agreement FPA n°2010–0009. This

research is also in the framework of the project ‘Integrated system to treat buffalo slurry, aimed to

recover water and safe energy’—STABULUM—funded, in agreement with the Decision of the

European Commission No C(2010) 1261, 2 March 2010, by the Agriculture Department of the

Campania Region in the context of the Programme of Rural Development 2007–2013, Measure

124 ‘Cooperation for development of new products, processes and technologies in the agriculture

and food sectors’.

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[20] P.H.M. Janssen, P.S.C. Heuberger, Calibration of process-oriented models, Ecol

Model. 83 (1993), 55–66.

[21] D.J. Hills and D.W. Roberts, Anaerobic digestion of dairy manure and field crop

residues. Agri. Wastes, 3, (1981), 179-189.

[22] W. Mussoline, G. Esposito, A. Giordano, P. Lens, The anaerobic digestion of rice

straw: A review. Crit. Rev. Env. Sci. Tec. 43, (2013), 895-915.

[23] N. Mora-Naranjo, J.A. Meima, A. Haarstrick, and DC. Hempel, Modelling and

experimental investigation of environmental influences on the acetate and methane

formation in solid waste, Waste Manage. 24 (2004), 763–773.

[24] S. Pommier, D. Chenu, M., Quintard, and X. Lefebvre, A logistic model for the

prediction of the influence of water on the solid waste methanization in landfills, Biotech.

Bioeng. 97 (2007), 473-482.

[25] D. Li, Y. Sun, Y. Guo, Z. Yuan, Y. Wang and F. Zhen, Continuous anaerobic

digestion of food waste and design of digester with lipid removal. Environ. Technol. 34

(2013), 2135-2143.

[26] Z. Bo, and H. Pin-Jing, Performance assessment of two-stage anaerobic digestion of

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kitchen wastes. Environ. Technol. 35 (2014), 1277-1285.

[27] Y. Lin, D. Wang, J. Liang and G. Li, Mesophilic anaerobic co-digestion of pulp and

paper sludge and food waste for methane production in a fed-batch basis. Environ.

Technol. 33 (2012), 2627-2633.

[28] D.B. Smith and B.C. Almquist, The anaerobic co-digestion of fruit and vegetable

waste and horse manure mixtures in a bench-scale, two-phase anaerobic digestion

system. Environ. Technol. 35 (2014), 859-867.

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Appendices

Table A.1

22,26,2013

23,26,2013

23,h2

,26,2013

22,26,2013

22,ac

,26,2013

21,26,2013

21,pro

44,26,2013

20,26,2013

20,C4

,26,2013

19,26,2013

19,fa

,26,2013

18,26,2013

18,aa

,26,2013

17,26,2013

17,su

122

22,2

28,119,116,2

3,28,119,1

15,

2,28,119,1

14,

244,444

244,4444

2,

1,28,119,1

10,,2,,,,

1,28,119,1

9,,2,,,

___,,

___,,

___

___

___

___

_

,

42

13

X ofDecay 23

X ofDecay 22

X ofDecay 21

X ofDecay 20

X ofDecay 19

X ofDecay 18

X ofDecay 17

)()1(1Hydrogen of Uptake16

)()1(1Acetate of Uptake15

)(43.0)1(57.0)1(1Propionate of Uptake14

1

1)(2.0)1(8.0)1(1Butyrate of Uptake13

1

1)(15.0)1(31.0)1(54.0)1(1Valerate of Uptake12

)(3.0)1(7.0)1(1LCFA of Uptake11

)()1()1()1()1()1(1Acids Amino of Uptake10

)()1()1()1()1(1Sugars of Uptake9

1(slowly) Lipids of Hydrolysis81(readily) Lipids of Hydrolysis7

1(slowly) Proteins of Hydrolysis61(readily) Proteins of Hydrolysis5

1(slowly) tesCarbohydra of Hydrolysis41(readily) tesCarbohydra of Hydrolysis3

Sludge oftion Disintegra2*OFMSW oftion Disintegra1

Process

][121110987654321Component

hXhdeci

iii

ii

acXacdeci

iii

ii

proXprodeci

iii

ii

cXcdeci

iii

ii

faXfadeci

iii

ii

aaXaadeci

iii

ii

suXsudeci

iii

ii

hhs

hhmbach

iiih

acacs

acacmbacac

iiiac

propros

proprombacpro

iiipropro

buvaC

bus

buCmbacCCC

vabuC

vas

vaCmbacCCCC

fafas

fafambacfafafa

aaaas

aaaambacaaaa

iiiaahaaaaacaaaaproaaaabuaaaavaaa

susus

susumbacsu

iiisuhsusuacsusuprosusubusu

SliSlihydlifalifa

RliRlihydlifalifa

SprSprhyd

RprRprhyd

SchSchhyd

RchRchhyd

SluSludis

sbkXcsI

IINICCHhacprobuvafaaasu

j

XKNC

XKNC

XKNC

XKNC

XKNC

XKNC

XKNC

IXSK

SKNYCY

IXSK

SKNYCY

IXSK

SKNYCYY

ISS

XSK

SKNYYY

ISS

XSK

SKNYYYY

IXSK

SKNYYY

IXSK

SKNYNCfYfYfYfYfY

IXSK

SKNYCfYfYfYfY

XKffXKffXKXKXKXK

XKaCKf

SSSSSSSSSSSS

dmkgCODrate

⋅−−

⋅−−

⋅−−

⋅−−

⋅−−

⋅−−

⋅−−

⋅⋅+

⋅−−−−

⋅⋅+

⋅−−−−

⋅⋅+

⋅−−−−−

⋅+

⋅⋅+

⋅−−−−

⋅+

⋅⋅+

⋅−−−−−

⋅⋅+

⋅−−−−

⋅⋅+

⋅−−−−−−−−

⋅⋅+

⋅−−−−−−−

⋅−⋅−⋅⋅⋅⋅

⋅⋅⋅

↓⋅⋅→

−=−=

−=−=

−=−=

−=−=

−=−=

−=−=

−=−=

−=

−=

−=

−=

−=

−−

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Table A.2

322,h2

,ac

,pro

44,C4

,fa

,aa

,su

122

22,2

,

2,

244,4

244,4

2,

1,

1,

___

___

___

___

___

___

_,,Pr,Pr,,,

,,,Pr,Pr,,,

24__Pr_Pr___

13

11X ofDecay 2311X ofDecay 22

11X ofDecay 2111X ofDecay 20

11X ofDecay 1911X ofDecay 18

11X ofDecay 17

Hydrogen of Uptake16

Acetate of Uptake15

Propionate of Uptake14

1

1Butyrate of Uptake13

1

1Valerate of Uptake12

LCFA of Uptake11

Acids Amino of Uptake10

Sugars of Uptake9

1(slowly) Lipids f o Hydrolysis81(readily) Lipids f o Hydrolysis7

1(slowly) Proteins f o Hydrolysis61(readily) Proteins f o Hydrolysis5

1(slowly) tesCarbohydra f o Hydrolysis41(readily) tesCarbohydra f o Hydrolysis3

1Sludge f otion Disintegra2*1OFMSW f otion Disintegra1

Process

][28272625242322212019181716151413Component

hXhdec

acXacdec

proXprodec

cXcdec

faXfadec

aaXaadec

suXsudec

hhs

hhmh

acacs

acacmac

propros

proprompro

buvaC

bus

buCmC

buvaC

vas

vaCmC

fafas

fafamfa

aaaas

aaaamaa

susus

susumsu

SliSlihyd

RliRlihyd

SprSprhyd

RprRprhyd

SchSchhyd

RchRchhyd

SluSludissXsluLirXsluLisXcrXslusXsluChrXsluCh

sbkXcXsXcLirXcLisXcrXcsXcChrXcCh

SluIhacproCfaaasuSLiRLiSRSChRCh

j

XKXKXK

XKXKXKXK

IXSK

SKY

IXSK

SKY

IXSK

SKY

ISS

XSK

SKY

ISS

XSK

SKY

IXSK

SKY

IXSK

SKY

IXSK

SKY

XKXKXKXKXKXK

XKffffffffffffaCKfffffffffffff

XXXXXXXXXXXXXXXC

dmkgCODrate

I

⋅−⋅−⋅−

⋅−⋅−⋅−⋅−

⋅⋅+

⋅

⋅⋅+

⋅

⋅⋅+

⋅

⋅+

⋅⋅+

⋅

⋅+

⋅⋅+

⋅

⋅⋅+

⋅

⋅⋅+

⋅

⋅⋅+

⋅

⋅−⋅−⋅−⋅−⋅−⋅−

⋅−⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅−

↓⋅⋅→ −−

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Figure Captions

Figure 1. Comparison of measured (points) and simulated (continuous line) data for experiments

with food waste: TS = 4.52% (A-D); TS = 12.92% (E-H) and TS = 19.02% (I-K). Figure 2. Comparison of measured (points) and simulated (continuous line) data for experiments

with rice straw: TS = 4.85% (A-D); TS = 14.86% (E-H); TS = 23.4% (I-K).

Figure 3.a. Linear correlation between disintegration kinetic constant and TS for rice straw and

food waste; 3.b. Linear correlation between propionate and acetate kinetic constants and TS

content for rice straw and food waste

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Table legends

Table 1. Substrate and Biomass variables in the model proposed by Esposito et al. (2011a, 2011b).

Table 2. Kinetic constants of the model proposed by Esposito et al. (2011a, 2011b).

Table 3. Calibrated kinetic constants for disintegration, acetate up-take and propionate up-take at

different TS concentrations for food waste and rice straw.

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Substrate

variables [ML-3] Symbol

Biomass

variables [ML-3] Symbol

Initial Substrate C Particulate inert Xi

Soluble Inert Si Propionate degraders Xpro

Total Propionate Spro Acetate Degraders Xac

Total Acetate Sac Butyrate and Valerate degraders Xb/v

Total Butyrate Sb Hydrogen degraders Xh

Total Valerate Sv Readily and slowly degradable carbohydrates

Xcb-S/Xcb-R

Gaseous Hydrogen

Shg Readily and slowly degradable lipids Xl-S /Xl-R

Gaseous Methane

Shm Readily and slowly degradable protein Xp-S/Xp-R

Inorganic carbon Sc LCFA Degraders XLCFA

Nitrogen SN Sugar Degraders Xs

LCFA SLCFA Amminoacids Degraders Xam

Sugar SS Sludge concentration Xsl

Amino acids Sam

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*only the dimensions of Ksbk is different, i.e.: [ML-2T-1].

Substrate Kinetic constants [T-1]*

Kinetic Process (ρj)

Complex Organic Substrate

Ksbk Disintegration of complex organic matter

Propionate Kpro Up-take of Propionate

Acetate Kac Up-take of acetate Total Valerate and Butyrate

Kc4 Up-take of Valerate and Butyrate

Hydrogen Kh Up-take of hydrogen Methane Km

Carbohydrate (slowly and readily biodegradable)

Kc-S/Kc-R Hydrolysis of carbohydrates

Lipids (slowly and readily biodegradable)

Kl-S/Kl-R

Hydrolysis of lipids

Proteins (slowly and readily biodegradable)

Kp-S/Kl-R Hydrolysis of proteins

LCFA KLCFA Up-take of LCFASugars Ks Up-take of Sugars

Amino acids Kam Up-take of amino acids

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Substrate TS

[%]

Kdis

[d-1]

RMSE Kac

[d-1]

RMSE Kpro

[d-1]

Food Waste

4.52 6.5 0.0072 8.47 0.0076 8.47

12.8 4 0.01 5.08 0.019 5.08

19.02 2 0.0065 2.46 0.011 2.46

Rice Straw

4.85 2.5 0.01 8.79 0.005 8.79 14.86 1.25 0.009 5.94 0.001 5.94

23.40 0.65 0.0073 3.51 0.001 3.51

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0 20 40 600

0.02

0.04

0.06

0.08

0.1

0.12

0.14

0.16

Time [d]

CH

4 [

mo

l]

(A)

0 0.05 0.1 0.15 0.20

0.02

0.04

0.06

0.08

0.1

0.12

0.14

0.16

Measured CH4 [mol]

Sim

ula

ted

CH

4 [

mo

l]

(B)

0 20 40 600

0.005

0.01

0.015

0.02

0.025

Time [d]

pro

pio

nat

e [m

ol]

(C)

0 20 40 600

0.005

0.01

0.015

0.02

0.025

0.03

0.035

Time [d]

acet

ate

[mo

l]

(D)

0 10 20 30 400

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

Time [d]

CH

4 [

mo

l]

(E)

0 20 40 600

0.005

0.01

0.015

0.02

0.025

0.03

0.035

0.04

0.045

Time [d]

pro

pio

nat

e [m

ol]

(G)

0 20 40 600

0.01

0.02

0.03

0.04

0.05

0.06

0.07

Time [d]

acet

ate

[mol

]

(H)

0 0.1 0.2 0.3 0.40

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

Measured CH4 [mol]

Sim

ula

ted

CH

4 [

mol

]

(F)

0 20 40 600

0.1

0.2

0.3

0.4

0.5

0.6

0.7

Time [d]

CH

4 [

mo

l]

(I)

0 0.2 0.4 0.6 0.80

0.1

0.2

0.3

0.4

0.5

0.6

0.7

Measured CH4 [mol]

Sim

ula

ted

CH

4 [

mo

l]

(J)

0 20 40 600

0.005

0.01

0.015

0.02

0.025

0.03

0.035

0.04

0.045

0.05

Time [d]

pro

pio

nat

e [m

ol]

(K)

0 20 40 600

0.01

0.02

0.03

0.04

0.05

0.06

0.07

Time [d]

acet

ate

[mo

l]

(L)

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0 20 40 600

0.02

0.04

0.06

0.08

0.1

0.12

0.14

Time [d]

CH

4 [

mo

l]

(A)

0 0.05 0.1 0.15 0.20

0.02

0.04

0.06

0.08

0.1

0.12

0.14

Measured CH4 [mol]

Sim

ula

ted

CH

4 [

mol

]

(B)

0 20 40 600

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8x 10

-3

Time [d]

pro

pion

ate

[mol

]

(C)

0 20 40 600

0.5

1

1.5

2

2.5

3x 10

-3

Time [d]

acet

ate

[mol

]

(D)

0 20 40 600

0.02

0.04

0.06

0.08

0.1

0.12

Time [d]

CH

4 [

mol

]

(E)

0 0.05 0.1 0.15 0.20

0.02

0.04

0.06

0.08

0.1

0.12

Measured CH4 [mol]

Sim

ula

ted

CH

4 [

mol

]

(F)

0 20 40 600

1

2

3

4

5

6

7x 10

-3

Time [d]

prop

iona

te [

mol]

(G)

0 20 40 600

1

2

3

4

5

6x 10

-3

Time [d]ac

etat

e [m

ol]

(H)

0 20 40 600

0.05

0.1

0.15

0.2

0.25

Time [d]

CH

4 [

mol

]

(I)

0 0.1 0.2 0.3 0.40

0.05

0.1

0.15

0.2

0.25

Measured CH4 [mol]

Sim

ula

ted C

H4 [

mol]

(J)

0 20 40 600

0.002

0.004

0.006

0.008

0.01

0.012

0.014

0.016

0.018

0.02

Time [d]

pro

pio

nat

e [m

ol]

(K)

0 20 40 600

1

2

3

4

5

6

7

8

9x 10

-3

Time [d]

acet

ate

[mol]

(L)

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a)

b)

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